Definition
Sector
A sector is a circle region enclosed by two radii and the arc between them.
What it means
Begin at the centre of a filled circle. Draw two straight radii to the boundary and keep the curved arc between their endpoints. The enclosed wedge-like region is a sector; it may be smaller than, equal to, or larger than a semicircle.
Remember it
Two radii are the straight sides; one arc is the curved side.
Example
Two perpendicular radii make a 90° central angle. Their smaller sector is 90 ÷ 360 = 1/4 of the disk.
Watch for
A region bounded by a chord and an arc is a circular segment, not a sector, unless the straight boundaries run from the centre as radii.
Common mix-up
The sector is the whole enclosed region, not only the arc and not only the central angle.
Exact meaning
A sector is a region of a disk bounded by two radii and the arc of the circle between their endpoints.